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Parameter scaling in the decoherent quantum-classical transition for chaotic systems

Arjendu K. Pattanayak·Bala Sundaram
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Abstract

The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $λ$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,λ,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $ζ= \hbar^αλ^βD^γ$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.

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Arjendu K. Pattanayak, Bala Sundaram. 2002-06-11. Parameter scaling in the decoherent quantum-classical transition for chaotic systems. https://doi.org/10.1103/physrevlett.90.014103

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